{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T08:58:12Z","timestamp":1762073892102,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,8]],"date-time":"2022-11-08T00:00:00Z","timestamp":1667865600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The purpose of the present study is to obtain regularity results and existence topics regarding an Eyring\u2013Powell fluid. The geometry under study is given by a semi-infinite conduct with a rectangular cross section of dimensions L\u00d7H. Starting from the initial velocity profiles (u10,u20) in xy-planes, the fluid flows along the z-axis subjected to a constant magnetic field and Dirichlet boundary conditions. The global existence is shown in different cases. First, the initial conditions are considered to be squared-integrable; this is the Lebesgue space (u10,u20)\u2208L2(\u03a9), \u03a9=[0,L]\u00d7[0,H]\u00d7(0,\u221e). Afterward, the results are extended for (u10,u20)\u2208Lp(\u03a9),\u00a0p&gt;2. Lastly, the existence criteria are obtained when (u10,u20)\u2208H1(\u03a9). A physical interpretation of the obtained bounds is provided, showing the rheological effects of shear thinningand shear thickening in Eyring\u2013Powell fluids.<\/jats:p>","DOI":"10.3390\/axioms11110625","type":"journal-article","created":{"date-parts":[[2022,11,9]],"date-time":"2022-11-09T02:34:52Z","timestamp":1667961292000},"page":"625","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Global Existence of Bounded Solutions for Eyring\u2013Powell Flow in a Semi-Infinite Rectangular Conduct"],"prefix":"10.3390","volume":"11","author":[{"given":"Saeed ur","family":"Rahman","sequence":"first","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad 22060, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4677-0970","authenticated-orcid":false,"given":"Jose Luis Diaz","family":"Palencia","sequence":"additional","affiliation":[{"name":"Department of Education, Universidad a Distancia de Madrid, 28400 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nomaq","family":"Tariq","sequence":"additional","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad 22060, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pablo","family":"Salgado S\u00e1nchez","sequence":"additional","affiliation":[{"name":"Spanish User Support and Operations Centre, Center for Computational Simulation, Universidad Polit\u00e9cnica de Madrid, 28223 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4017-3067","authenticated-orcid":false,"given":"Julian Roa","family":"Gonzalez","sequence":"additional","affiliation":[{"name":"Department of Education, Universidad a Distancia de Madrid, 28400 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Khan, Z., Rasheed, H., Abbas, T., Khan, W., Khan, I., Baleanu, D., and Nisar, K.S. (2020). Analysis of Eyring\u2014Powell fluid flow used as a coating material for wire with variable viscosity effect along with thermal radiation and joule heating. Crystals, 10.","DOI":"10.3390\/cryst10030168"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"143968","DOI":"10.1155\/2014\/143968","article-title":"Analysis of Eyring-Powell fluid in helical screw rheometer","volume":"2014","author":"Siddiqui","year":"2014","journal-title":"Sci. World J."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"924","DOI":"10.1080\/01430750.2019.1679253","article-title":"Magneto-bioconvection of Powell-Eyring nanofluid over a permeable vertical stretching sheet due to gyrotactic microorganisms in the presence of nonlinear thermal radiation and Joule heating","volume":"43","author":"Dulal","year":"2022","journal-title":"Int. J. Ambient. Energy"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"996","DOI":"10.1166\/jon.2022.1886","article-title":"Entropy optimization and heat transfer analysis of magneto-bioconvective Powell\u2013Eyring nanofluid with nonlinear thermal radiation and chemical reaction over a stretching sheet","volume":"11","author":"Kanta","year":"2022","journal-title":"J. Nanofluids"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1016\/j.jmmm.2015.01.088","article-title":"Numerical analysis of magnetic field effects on Eyring-Powell fluid flow towards a stretching sheet","volume":"382","author":"Akbar","year":"2015","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.jmmm.2015.11.059","article-title":"MHD peristaltic transport of Eyring-Powell fluid with heat\/mass transfer: Wall properties and slip conditions","volume":"404","author":"Hina","year":"2016","journal-title":"J. Magn. Magn. Mater."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Bhatti, M., Abbas, T., Rashidi, M., Ali, M., and Yang, Z. (2016). Entropy generation on MHD Eyring-Powell nanofluid through a permeable stretching surface. Entropy, 18.","DOI":"10.3390\/e18060224"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"772","DOI":"10.1139\/cjp-2018-0586","article-title":"Analysis of modified Fourier law in flow of ferromagnetic Powell\u2013Eyring fluid considering two equal magnetic dipoles","volume":"97","author":"Zubair","year":"2018","journal-title":"Can. J. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/j.ijheatmasstransfer.2013.05.049","article-title":"Self-similar solutions for the flow and heat transfer of Powell-Eyring fluid over a moving surface in a parallel free stream","volume":"65","author":"Jalil","year":"2013","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1166\/jctn.2015.3703","article-title":"Application of Eyring-Powell fluid model in peristalsis with nano particles","volume":"12","author":"Akbar","year":"2015","journal-title":"J. Comput. Theor. Nanosci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1253","DOI":"10.1139\/cjp-2018-0732","article-title":"Heat transfer analysis of magneto-Eyring\u2013Powell fluid over a nonlinear stretching surface with multiple slip effects: Application of Roseland\u2019s heat flux","volume":"97","author":"Majeed","year":"2019","journal-title":"Can. J. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"584","DOI":"10.1016\/j.apnum.2009.04.010","article-title":"Numerical treatment of Powell-Eyring fluid flow using method of satisfaction of asymptotic boundary conditions","volume":"59","author":"Patel","year":"2009","journal-title":"Appl. Numer. Math."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.rinp.2014.03.004","article-title":"Mixed convection flow of Eyring-Powell fluid along a rotating cone","volume":"4","author":"Nadeem","year":"2014","journal-title":"Results Phys."},{"key":"ref_14","first-page":"313","article-title":"Boundary layer flow of an Eyring-Powell model fluid due to a stretching cylinder with variable viscosity","volume":"20","author":"Malik","year":"2013","journal-title":"Sci. Iran."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1337","DOI":"10.1016\/j.asej.2014.06.002","article-title":"Radiation effect on boundary layer flow of an Eyring-Powell fluid over an exponentially shrinking sheet","volume":"5","author":"Ara","year":"2014","journal-title":"Ain Shams Eng. J."},{"key":"ref_16","first-page":"327","article-title":"Flow of an Eyring-Powell non-Newtonian fluid over a stretching sheet","volume":"3","author":"Javid","year":"2012","journal-title":"Chem. Eng. Commun."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1899","DOI":"10.1016\/j.rinp.2017.06.002","article-title":"Modeling and simulation for 3D magneto Eyring-Powell nanomaterial subject to nonlinear thermal radiation and convective heating","volume":"7","author":"Khan","year":"2017","journal-title":"Results Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2859","DOI":"10.1016\/j.jtice.2014.08.018","article-title":"MHD flow of Powell-Eyring fluid over a rotating disk","volume":"45","author":"Khan","year":"2014","journal-title":"J. Taiwan Inst. Chem. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"621","DOI":"10.1016\/j.aej.2016.11.006","article-title":"Solution of the boundary layer flow of an Eyring-Powell non-Newtonian fuid over a linear stretching sheet by collocation method","volume":"56","author":"Rahimi","year":"2016","journal-title":"Alex. Eng. J."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/j.jde.2004.07.002","article-title":"On the regularity of weak solution to the magnetohydrodynamic equations","volume":"213","author":"He","year":"2005","journal-title":"J. Differ. Equations"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"947","DOI":"10.1080\/00036811.2011.556626","article-title":"On regularity criteria in terms of pressure for the 3D Viscous MHD equations","volume":"91","author":"Duan","year":"2012","journal-title":"Appl. Anal."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1803","DOI":"10.1016\/j.aim.2010.08.017","article-title":"Global regularity for the 2D MHD equations with mixed partial dissipation and magnetic diffusion","volume":"226","author":"Cao","year":"2011","journal-title":"Adv. Math."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1496","DOI":"10.1016\/j.matpur.2005.07.003","article-title":"A new regularity criterion of weak solutions to the Navier-Stokes equations","volume":"84","author":"Zhou","year":"2005","journal-title":"J. Math. Pures Appl."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"e201900200","DOI":"10.1002\/zamm.201900200","article-title":"Liouville-type theorems for the 3D stationary Hall-MHD equations","volume":"100","author":"Li","year":"2020","journal-title":"ZAMM-J. Appl. Math. Mech."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"474","DOI":"10.1016\/j.jmaa.2016.01.023","article-title":"A regularity criterion for the Navier\u2013Stokes equations based on the gradient of one velocity component","volume":"437","author":"Skalak","year":"2016","journal-title":"J. Math. Anal. Appl."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1139\/cjp-2016-0624","article-title":"Global existence criteria for Sisko fluid in annular region","volume":"95","author":"Rahman","year":"2017","journal-title":"Can. J. Phys."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1007\/s00021-010-0039-5","article-title":"Logrithmically improved regularity criteria for the Navier-Stokes and MHD equations","volume":"13","author":"Fan","year":"2011","journal-title":"J. Math. Fluid Mech."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"728","DOI":"10.3906\/mat-1502-44","article-title":"Global regularity for unsteady flow of third grade fluid in an annular region","volume":"40","author":"Rahman","year":"2016","journal-title":"Turk. J. Math."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1007\/BF01084616","article-title":"Estimates of the solutions of the nonstationary Navier-Stokes system","volume":"8","author":"Solonnikov","year":"1977","journal-title":"J. Sov. Math."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"4094","DOI":"10.1002\/mma.7013","article-title":"Dispersive of propagation wave solutions to unidirectional shallow water wave Dullin\u2013Gottwald\u2013Holm system and modulation instability analysis","volume":"44","author":"Bilal","year":"2021","journal-title":"Math. Methods Appl. Sci."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"105069","DOI":"10.1016\/j.rinp.2021.105069","article-title":"Weakly nonlinear electron-acoustic waves in the fluid ions propagated via a (3+1)-dimensional generalized Korteweg\u2014de-Vries\u2013Zakharov\u2013Kuznetsov equation in plasma physics","volume":"33","author":"Rehman","year":"2022","journal-title":"Results Phys."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1016\/j.joems.2013.02.009","article-title":"Radiative effects in a three dimensional flow of MHD Eyring-Powell fluid","volume":"21","author":"Hayat","year":"2013","journal-title":"J. Egypt. Math. Soc."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1038\/154427a0","article-title":"Mechanisms for the relaxation theory of viscosity","volume":"3909","author":"Powell","year":"1944","journal-title":"Nature"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"104152","DOI":"10.1016\/j.jtice.2021.11.019","article-title":"Theoretical analysis of modified eyring powell fluid flow","volume":"132","author":"Oke","year":"2022","journal-title":"J. Taiwan Inst. Chem. Eng."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/BF02392215","article-title":"Hp spaces of several variables","volume":"129","author":"Fefferman","year":"1972","journal-title":"Acta Math."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/11\/625\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:12:42Z","timestamp":1760145162000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/11\/625"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,8]]},"references-count":35,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["axioms11110625"],"URL":"https:\/\/doi.org\/10.3390\/axioms11110625","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2022,11,8]]}}}